1. Field of the Invention
Embodiments disclosed herein relate to comparing the flow rates of two or more fluids. In particular, embodiments disclosed herein relate to comparing the effect of a drag reduction agent in a fluid. More particular still, embodiments disclosed herein relate to screening drag reduction agents to determine whether the drag reduction agent functions as intended according to defined variables.
2. Background Art
Drag reduction is defined as the reduction of a fluid's frictional resistance in turbulent flow and thus increase in pumpability of the fluid caused by the addition of small amounts of another substance, frequently high molecular weight polymers, to the fluid. Specifically, drag reduction is a reduction in the pressure drop over some length of a pipeline when traces of a drag reduction agent are dissolved in the pipeline fluid. The key factors governing the amount of drag reduction achievable in a given system are: solubility of the agent in the continuous phase; effectiveness in dispersing the agent; molecular weight of the agent; and concentration of the agent. The phenomenon of drag reduction has been used in a variety of pipelines to reduce shear stresses and thereby decrease the amount of pump power input necessary to flow fluids therethrough.
When fluids travel through a pipe, a velocity profile develops that varies from zero velocity (at the wall of the pipe) to a maximum velocity (at the centerline of the pipe). This profile is caused by viscid flow properties that create shear layers in the fluid. At very low bulk flow velocities, these shear layers are well-ordered laminae, and there is no transverse flow between the layers, which is described as laminar flow. Pressure drop per unit length of pipe is also low. As bulk flow velocities increase, the laminar nature of the flow begins to break down. At the interface between laminae, the local flow begins to tumble due to shearing, creating transverse flow, in which faster moving particles are transported into regions of lower velocity and vice-versa. This turbulent flow causes greater pressure drop per unit length of pipe and demands higher pumping energy into the flow to maintain the bulk velocity of the flow.
These two flow regimes are defined by Reynolds number (Re), the ratio of the fluid body forces to viscous forces. Values of Re of less than 2000 include the laminar flow regime for pipes. As Re increases, pipe flow transitions from laminar to turbulent over a range of values from 2,000 to 10,500 and is fully turbulent above 10,500. Typically, drag reducers are very high molecular weight hydrocarbon polymers suspended in a dihydrocarbon solvent. When added to crude or refined products in a pipeline, these polymers reduce transverse flow gradients, effectively creating a laminar flow in the pipe. This is especially true close to the pipe walls where the axial flow velocity profile has a very steep gradient in which significant pressure losses occur. Lowering these internal fluid losses increases the bulk throughput of the pipeline for a given pumping energy.
Typically, the amount of drag reducer in a fluid is small, on the order of one part per million. The drag reducer molecular chain is very fragile, however. The chain can be sheared or broken as the chain passes through both natural and/or manmade features, such as bends in a pipeline, valves, piping branches, and when the flow goes through a pumping station. Thus, the chain may be broken by passage through any type of stream. Once the molecular chain is broken, the drag reducer is immediately degraded. The extent of drag reduction is limited by this degradation of drag reducing agents into smaller, less-effective chains as the polymers travel downstream. It has been show that the rate of this degradation is strongly dependent on diameter. As industrial pipelines are often orders of magnitude larger than laboratory-scale pipelines, diameter is an important consideration in industrial pipeline scale-up. For example, as pipeline diameter increases from that of fire hoses (50 mm) to the Trans-Alaska Pipeline System (1194 mm), operating at the same wall shear stress of approximately 40 Pa, the apparent first-order rate constant for polymer degradation decreases by three orders of magnitude.
In dilute solution, non-ionic vinyl polymers, such as polyethylene oxide, form random coils independently of one other. In turbulent flow, it is theorized that the polymer chains extend to bridge turbulent “bursts,” thereby decreasing turbulence production and thence, presumably, the wall shear stress. For example, turbulent jets of water and polyethylene oxide solution were compared to show that the polymer chains suppressed small-scale eddies.
In 1970, a series of experiments measured drag reduction at different Reynolds values and concentrations. It was discovered that, for low turbulent Re, as the concentration of polymer increases, the friction coefficient decreases, thus implying an increase in drag reduction. It was also shown that drag reduction was linearly correlated to concentration for concentrations below 50 ppm, suggesting that the polymer chains work independently of one another to cause drag reduction.
Drag reduction efficiency has also been strongly correlated with the molecular weight of the polymer. At higher molecular weights, the onset of drag reduction begins at lower Reynolds number values. For this reason, high molecular weight polymers have been favored for commercial applications. Experiments with polyethylene oxide also support the requirements of long molecules of high molecular weight, with few side branches and good solubility as ideal polymers for drag reduction.
The injection of long-chain polymers into pipe flow is the most widely-studied and commercially applicable form of drag reduction. Drag reducers are often used in pipeline systems to facilitate the flow of crudes, diesel fuels, and automotive gasoline, and are also used in the formulation of thixotropic fluid systems used in wellbores. The amount of drag reduction agent required in ppm to achieve a certain flow increase depends upon many factors. For a particular pipeline, depending upon the liquid viscosity and gravity and the Reynolds number, drag reduction effectiveness effectiveness varies with flow rate.
Currently, the definitive apparatus used for testing drag reduction is a flow-loop test, the results of which can be scaled-up to a full-scale pipe, otherwise known as a scale-up flow loop (“SUFL”). A SUFL is built from small-diameter conduits to limit laboratory space and fluid volumes, and is used to predict frictional pressure losses for the same fluid in large-diameter conduits and precisely determine the drag reduction of a fluid and/or a fluid additive. Flow-loop and sectional geometry include the length, hole diameter, and external and internal pipe diameters, respectively. Flow loops are considered to have a singular geometry, although some are configured with serial and parallel test sections of different diameters.
As fluid density and rheological properties are maintained constant during SUFL testing, the fluid temperature should not vary appreciably during the entire test procedure. Thus, for flow-loop experiments, test-section geometry and mud properties do not change. To calculate pressure losses in a pipeline or well, the fluid passes through depth intervals (or section lengths) at a constant flow rate. For a wellbore, drill string and annular pressures would be the summation of the calculated pressures in each row for different flow-rate values.
While SUFL testing may produce accurate drag information, the preparation and operation requires significant investments of time and money. First, the SUFL typically requires five-gallon sample of testing fluid, which could be costly depending on the cost of the fluid and/or the additive. Additionally, one test-run lasts about 1 hour per sample. Once a sample fluid is tested, the system must be flushed of all remaining fluid to prepare for the next test sample, adding additional time to the testing process. Economic shortcomings also derive from the high cost of energy required for the operation and cleaning of the SUFL, as well as the high cost of parts required to assemble a SUFL. Due to the increasing costs of producing, testing, and implementing wellbore fluids, the industry needs a streamlined testing system and method that uses less energy, sample volume, and time.
Accordingly, there exists a continuing need for an effective test to measure the impact on drag by drag reduction agents.